We give a deterministic $O(m\log^{2/3}N)$-time algorithm for single-source
shortest paths (SSSP) on directed graphs with real non-negative edge weights in
the comparison-addition model. This is the first result to break the $O(m+n\log
N)$ time bound of Dijkstra’s algorithm on sparse graphs, showing that
Dijkstra’s algorithm is not optimal for SSSP.

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